Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic part 14 pptx
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 2 docx
... the cooperation participants.
Let the two manipulators hold the object from the previous example and let
22 Multi-Arm Cooperating Robots
acting forces on the object, F
c1
and F
c2
and, by small ... col(r
ex
ci
,r
ey
ci
,r
ez
ci
) ∈ R
3
with respect to
14 Multi-Arm Cooperating Robots
presentation of the consistent mathematical procedure of modeling statics and dy-
namics of th...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 3 pot
... nodes and
system of forces) and the dimensional part (dimension [position/force]) that is in-
versely proportional to the elasticity module of the material and characteristics of
the cross-section ... contacts. The ‘non-uniqueness’ appears only in the description of the part of
the system between the manipulator tips (grippers) and object. This suggests the
30 Multi-Arm Coopera...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 4 ppt
... position and force of the
manipulated object are X
0
, Y
0
and F
I 0
, whereas Y
i
, F
i
, F
ci
and τ
i
, i = 1, 2are
the displacements of contact points, elastic forces, contact forces and manipula-
tor ... state quantities are the po-
sition and velocity of the object MC Y
2
and
˙
Y
2
. The elastic forces are at the same
time the contact forces F
1
=−f
c1
and F
3
=−f
c2
(f
c1...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 5 pdf
... direc-
tion y
z
i
. The total potential energy of the elastic system is only its deformation
82 Multi-Arm Cooperating Robots
73
efficient on-line algorithms for connecting such finite elements and ... stiffness matrix; y
0
and F
e0
are the vectors of displacements and forces at the
manipulated object MC, whereas y
c
and F
ec
are the expanded vectors of displace-
ments and forces...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 6 ppsx
... contact of the manipulator tips and object in w hich no change of con-
tact point on the manipulated object is allowed, whereas the forces and moments
106 Multi-Arm Cooperating Robots
93
or, in ... )
∂Y
=
1
2
∂
∂Y
(Y
T
¯π
a
(Y )Y )
90 Multi-Arm Cooperating Robots
one gets
r
Ija
= r
Iia
− A(a)ρ
ij a
. (146 )
If the positions of all the nodes r
Ija
, j = 0, 1, ,m, are expressed as a...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 8 doc
... Simulation results for τ
1
1
= 50 [Nm] and τ
1
2
=−50 [Nm]
132 Multi-Arm Cooperating Robots
part referring to the physical quantity used in modeling and the number indicat-
ing the ordinal number of the ... F
y
1
and moment
M
1
in the direction of the displacements Y
x
1
, Y
y
1
and ϕ
1
of the first contact point.
136 Multi-Arm Cooperating Robots
131
Figure 22c. Simulation re...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 9 ppt
... Y
0
c
, Y
0
0
, velocities
˙
Y
0
c
,
164 Multi-Arm Cooperating Robots
can be calculated as a function of non-selected vectors of the followers’ displace-
ments and known vector. Let the displacement ... equations (239) represents non-holonomic constraints. Solv-
ing the nominal motion assumes the explicit calculation of the necessary contact
156 Multi-Arm Cooperating Robots
149
+[...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 10 pps
... y
s
s0
=
col(y
s
s
,y
s
0
) and the force at the MC of the manipulated object at the end of grip-
168 Multi-Arm Cooperating Robots
Figure 30. Nominals for manipulated object general motion
184 Multi-Arm Cooperating ... required, the contact forces can be given
174 Multi-Arm Cooperating Robots
Figure 32. Simulation results for motion (open-loop cooperative system)
186 Multi-Arm...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 11 pptx
... of time for the
non-controlled object and of time and state for the controlled object. For the con-
200 Multi-Arm Cooperating Robots
For a linear system of n
x
ordinary first-order differential ... torques τ ,andthe
204 Multi-Arm Cooperating Robots
203
– elastic;
• in view of their redundanc y
– non-redundant, and
– redundant;
• in view of joint compliance
– with non-compliant jo...
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